Multidimensional treatment of photon emission from accretion discs around black holes

We consider photon emission from a supercritical accretion disc in which photons in the inner regions are trapped and advected in towards the centre. Such discs are believed to be present in failed supernovae and gamma-ray bursts, and possibly also in ultraluminous X-ray sources. We show that the luminosity from a supercritical accretion disc is proportional to the logarithm of the mass accretion rate when the vertical profile of the matter density is exponential. We obtain analytical results also for other density profiles, but the dependence of the luminosity on the accretion rate is no longer logarithmic.